1. Field of the Invention
The present invention relates to a method for thermally analyzing a material, comprising the steps of providing a sample of said material, providing a heat source so as to cause a flow of heat between said sample and said heat source, controlling a heating condition of said heat source as a function of time, measuring a signal representative of said heat flow between said sample and said heat source and a signal representative of a temperature associated with said heat flow, and evaluating a functional relation between said measured heat flow and temperature signals; and to an apparatus adapted for carrying out said method.
2. Description of the Related Art
In the thermal analysis of materials, a sample of the material is heated by the heat source, and the flow of heat between the heat source and the sample is evaluated to thereby derive structural and compositional information about the material, in particular heat capacity, heat of reaction phase transitions, onset temperatures, etc. In particular, for the sake of accuracy and dynamic range, differential methods, e. g. differential scanning calorimetry (DSC), are being used. In these differential methods, a reference material is arranged in the heat flow symmetrically with respect to the sample to be analyzed, and the analysis is performed on the basis of the differential heat flow between the sample and reference materials.
EP 0 559 362 A1 discloses a differential method wherein the temperature of the heat source is controlled in accordance with a predetermined temperature program so as to cause said heat source temperature to vary in correspondence with a linear rise of temperature superposed by a periodic temperature modulation. A deconvolution technique is used to derive from the differential heat flow signal two separate signal components caused by the linearly changing component and the modulation component of the heat source temperature, respectively.
WO95/33199 and WO95/33200 similarly disclose differential methods wherein a temperature of the heat source is driven through a predetermined temperature program, said temperature program comprising two linearly changing parts of the same time duration in the first case and a linearly changing part superposed by a periodically changing part in the second case. The differential heat flow signal and a phase difference between the differential heat flow signal and the programmed temperature of the heat source are evaluated to separately derive a real and an imaginary signal portion.
In these conventional methods, the thermal excitation of the sample is due to linear or periodic functions, or combinations of both. As a consequence, the subgroup of thermal events which selectively induced by the excitation frequency among the entire group of all possible events. These selectively excited events are those having the same frequency or, depending on the type of excitation and condition of the sample, events corresponding to a multiple integer of the excitation frequency (higher harmonics). The response of the sample is frequency-dependent.
It is an object of the present invention to provide for a method for thermally analysing a material capable of detecting responses from events without being restricted to frequency-selective excitation. It is a further object to provide for an apparatus which is capable of carrying out this method.
Having regard to the method, this object is attained in accordance with the invention in that said controlling step comprises to stochastically modify said heating condition.
According to the present invention, by stochastically modifying a heating condition, e. g. heating power or heating temperature of the heat source, excitation is not selectively limited to a certain frequency. The response of the material sample depends on how events in the material sample are time-correlated with the excitation. The stochastic excitation allows to directly measure the relaxation function. The relaxation function describes the time response of the material to a pulse-shaped disturbance. The time-dependent excitation of the sample material as opposed to frequency-dependent excitation causes different characteristics and properties of the sample material and the heat transfer path to be detected.
Theoretically, the results of conventional frequency-dependent excitation and stochastic excitation in accordance with the present invention may be mathematically related by means of Fourier transformation. However, this is impossible in practice. To calculate the mathematical relation would require error-free measured values in a frequency and time range between zero and infinity. Since this cannot be realized in practice, the calculation of the mathematical relation suffers loss of information. Moreover, the relation would only apply if the sample material exhibited a linear behaviour during the measurement. However, the assumption of linear behaviour can generally not be made.
The terms xe2x80x9cheatingxe2x80x9d, xe2x80x9cheat flowxe2x80x9d, xe2x80x9cheat sourcexe2x80x9d and related terms are to be understood in the context of the present specification to mean either heating or cooling. In the latter case, the xe2x80x9cheat sourcexe2x80x9d will e. g. be a source of cooling agent thermally coupled to the sample.
In one embodiment of the invention said controlling step is based on a first control input for causing said heat source to assume a predetermined temperature as a function of time and a second control input for stochastically modifying the heating condition of said heat source caused by said first control input.
The second control input for stochastically modifying the heating condition may be defined in terms of a corresponding modification of the temperature, heating rate, heating power or heat flow of the heat source . It may be generated numerically or electronically.
The first control input for causing the heat source to assume a predetermined temperature as a function of time may correspond to the isothermic case where the heating rate is zero and the temperature of the heat source is controlled to be constant at a selected temperature value. In the more general case, the first control input is so that the corresponding temperature-versus-time function varies with time considerably slower than the stochastically varying second control input does. A particularly interesting specific case includes to vary the temperature of the heat source by the first control input in accordance with a linear temperature program, which means a selected constant heating rate.
In another embodiment of the invention, the method further comprises the steps of measuring a temperature of said heat source and using a signal representative of a difference between a superposition of said first control input with said second control input and said measured temperature of said heat source as a heating power control signal for said heat source. In this case, the measured temperature of the heat source is compared with the superposition of the first and second control inputs, and the difference resulting from this comparison is used to control the heating power of the heat source. In this case, the superposed first and second control inputs correspond to the heating temperature of the heat source.
In still another embodiment, the method in accordance with the invention comprises the steps of measuring a temperature of said heat source, filtering said measured temperature of said heat source to thereby derive an average temperature related to the unmodified heating power of said heat source and using a signal representative of a superposition of said second control input with a difference between said first control input and said average temperature as a heating power control signal for said heat source. In this case, the average temperature of the heat source is compared with the first control input, and the second control input is superposed on the result of the comparison to control the heating power of the heat source. Accordingly, the first control input corresponds to the average temperature of the heat source while the second control input causes a stochastic modification of the average temperature corresponding to the first control input.
Preferably, said signal representative of heat flow is a differential signal corresponding to a difference of heat flows between said sample and said heat source and a reference material and said heat source. This provides for high accuracy and wide dynamic range since only the difference in heat flowing into or out of said sample as compared to the heat flowing into or out a known reference material is used for the purposes of analysis, and there is no need for an absolute measurement.
While each of heat source temperature or sample temperature could be used as a temperature associated with the heat flow, it is preferred that a temperature of said reference material is measured and is used as said signal representative of a temperature associated with said heat flow.
According to another essential aspect, the method according to the present invention comprises the steps of deriving an average component of at least one of said measured heat flow and a heating rate derived from said measured temperature associated with said heat flow over a selected interval of time, deriving a dynamical component of at least one of said heat flow and heating rate as a difference between said measured heat flow or derived heating rate, respectively, and said respective derived average component, deriving an average temperature of said measured temperature associated with said heat flow over said selected interval of time and representing at least one of said dynamical components as a function of said derived average temperature.
The dynamical component obtained by this type of evaluation is related to the stochastic variation of the heating power of the heat source while the average component is related to a heating power controlled by the first control input with the stochastic fluctuations caused by the second control input being smoothed out. The length of the time interval selected for the averaging process is dimensioned in accordance with the type of measurement so as to be sufficiently long for obtaining a reasonable average, but not so long as to suppress the excitation responses being looked for in the analysis of the material.
In order to perform the method in accordance with the invention, an apparatus for thermally analyzing a material comprising a heat source, a sample holder having a sample position arranged so as to enable a flow of heat between said heat source and a sample in said sample position, a controller for controlling a heating condition of said heat source as a function of time, means for measuring a signal representative of said heat flow between said sample in said sample position and said heat source, means for measuring a signal representative of a temperature associated with said heat flow and means for evaluating a functional relation between said measured heat flow and temperature signals is in accordance with the invention characterized in that said controller comprises means for stochastically modifying said heating condition. The controller may be implemented by a microcomputer.
In one embodiment, said controller comprises means for setting a first control signal representing a selected temperature program of said heat source as a function of time and means for generating a second control signal stochastically varying in time to thereby stochastically modify said heating condition caused by said first control signal.
Both of the means for setting the first and second control signals may be implemented by means of a microcomputer. In this case, the second control signal may be generated on the basis of a random number generator implemented in the microcomputer. Alternatively, dedicated electronics may be used to generate the second control signal stochastically varying in time.